Generalized deductive systems in subregular varieties

Ivan Chajda

Displaying similar documents to “Generalized deductive systems in subregular varieties”

Diamond identities for relative congruences

Gábor Czédli (1995)

Archivum Mathematicum

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For a class $K$ of structures and $A \in K$ let ${C o n}^{*} (A)$ resp. ${C o n}^{K} (A)$ denote the lattices of $*$ -congruences resp. $K$ -congruences of $A$ , cf. Weaver [25]. Let ${C o n}^{*} (K) : = I {{C o n}^{*} (A) : A \in K}$ where $I$ is the operator of forming isomorphic copies, and ${C o n}^{r} (K) : = I {{C o n}^{K} (A) : A \in K}$ . For an ordered algebra $A$ the lattice of order congruences of $A$ is denoted by ${C o n}^{<} (A)$ , and let ${C o n}^{<} (K) : = I {{C o n}^{<} (A) : A \in K}$ if $K$ is a class of ordered algebras. The operators of forming subdirect squares and direct products are denoted by $Q^{s}$ and $P$ , respectively. Let $λ$ be a lattice identity and let $Σ$ be a set of lattice identities....

k-Normalization and (k+1)-level inflation of varieties

Valerie Cheng, Shelly Wismath (2008)

Discussiones Mathematicae - General Algebra and Applications

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Let τ be a type of algebras. A common measurement of the complexity of terms of type τ is the depth of a term. For k ≥ 1, an identity s ≈ t of type τ is said to be k-normal (with respect to this depth complexity measurement) if either s = t or both s and t have depth ≥ k. A variety is called k-normal if all its identities are k-normal. Taking k = 1 with respect to the usual depth valuation of terms gives the well-known property of normality of identities or varieties. For any variety...

Congruence classes in regular varieties.

Bělohlávek, R., Chajda, I. (1999)

Acta Mathematica Universitatis Comenianae. New Series

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A note on normal varieties of monounary algebras

Ivan Chajda, Helmut Länger (2002)

Czechoslovak Mathematical Journal

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A variety is called normal if no laws of the form $s = t$ are valid in it where $s$ is a variable and $t$ is not a variable. Let $L$ denote the lattice of all varieties of monounary algebras $(A, f)$ and let $V$ be a non-trivial non-normal element of $L$ . Then $V$ is of the form $M o d (f^{n} (x) = x)$ with some $n > 0$ . It is shown that the smallest normal variety containing $V$ is contained in $H S C (M o d (f^{m n} (x) = x))$ for every $m > 1$ where $C$ denotes the operator of forming choice algebras. Moreover, it is proved that the sublattice of $L$ consisting of all normal...